In the semiconductor manufacturing industry, it is necessary to achieve precise control of the quantity, temperature and pressure of one or more reactant materials which are delivered in the gaseous state to a reaction chamber. Some process reactants, such as nitrogen gas, are relatively easy to deliver in a controlled manner at the temperatures and pressures required for the reaction to occur. Other reactants, however, may be highly corrosive, toxic, pyrophoric, or unstable at the temperatures and/or pressures at which delivery to the reaction chamber is required. Such characteristics of the reactants make their accurate and controlled delivery to a reaction chamber extremely difficult to achieve.
Mass flow controllers (hereinafter, "MFCs") are widely used in the industry to control the delivery of process reactants. Two broad categories of MFCs, thermal and pressure-based, have been developed to handle the diverse delivery requirements of a wide variety of process reactants. Thermal mass flow controllers operate on the principle that the rate of heat transfer from the walls of a flow channel to a fluid flowing in laminar flow within the channel is a function of the difference in temperatures of the fluid and the channel walls, the specific heat of the fluid, and the mass flow rate of the fluid. Thus, the rate of mass flow of a fluid (in the laminar flow regime) can be determined if the properties of the fluid and the temperatures of the fluid and tube are known.
Thermal MFCs generally include one or more heating elements wound around a relatively narrow, thin-walled tube through which a laminar fluid flow is established and maintained. The heating elements generally have a high thermal coefficient of resistance and thus also accurately sense the temperature of the fluid in the tube. As long as laminar flow is maintained, the mass flow rate of the fluid can be accurately determined from changes in resistance of the heating elements in response to changes in the temperature of the fluid as it flows through the tube.
Thermal MFCs have some inherent limitations which make them unsuitable for use with certain reactants or under certain flow conditions. For example, reactants which have relatively low vapor pressures, i.e., below about 100 torr, or which thermally decompose at relatively low temperatures, i.e., below 100 to 150 degress C., cannot be controllably delivered in vapor form with thermal MFCs. Such reactants form gases which are unstable at the pressures and temperatures at which delivery is required and are thus likely to decompose or condense in the delivery lines prior to reaching the process chamber. In addition, the response of a thermal MFC to changes in fluid flow rate may be relatively slow due to the thermal characteristics of the tube and the time required for the fluid to reach equilibrium temperature distribution conditions as flow rate changes occur. This slow response can be alleviated somewhat by maintaining a constant temperature profile about the tube. A thermal MFC which uses three heating elements to establish a known temperature profile of the fluid and provide an output signal which is linearly proportional to mass flow rate is disclosed in U.S. Pat. No. 4,464,932 to Ewing et al.
On the other hand, pressure-based MFCs operate on the principle that changes in fluid pressure induce deflections in a deformable electrode, the deflections causing corresponding changes in the electrical capacitance of the deformable electrode and a stationary one coupled therewith. Pressure-based MFCs, which include, for example, capacitance manometer pressure transducers, are capable of controllably delivering process reactants at inlet pressures of less than 1 torr to greater than atmospheric pressure (760 torr).
Distinct flow regimes of a flowing fluid are recognized and defined by different pressure profiles within the fluid. Molecular flow occurs at fluid pressures of less than about 1 torr, and the flow rate of a fluid through a flow restrictive device, such as a nozzle, in the molecular flow regime is proportional to the pressure drop across the flow restrictive device. Laminar flow occurs at fluid pressures of greater than about 10 torr, and the flow rate of a fluid through a flow restrictive device in the laminar flow regime is proportional to the difference of the squares of the upstream and downstream pressures.
The pressure-based mass flow controllers disclosed in, for example, U.S. Pat. No. 3,851,526 to Drexel and U.S. Pat. No. 5,445,035 to Delajoud operate on the assumption that the fluid flow remains laminar. This assumption of laminar fluid flow limits the utility of these pressure-based MFCs to laminar flow conditions and leads to inaccuracies when such MFCs are used to characterize non-laminar flows.
In another pressure-based mass flow controller, exemplified by the Model 1150 mass flow controller manufactured and sold by the assignee of the present invention, the necessity for assuming laminar flow is avoided by creation of a viscous choked flow condition in the system. To establish viscous choked flow, two pressure reservoirs are created along the flow path of the fluid, for example, by introducing a restriction in the diameter of the flow path using means for defining a flow restrictive aperture, such as an orifice or nozzle. In the reservoir upstream of the flow restrictive aperture the fluid has a pressure p.sub.1 and a density .rho..sub.1, and in the reservoir downstream of the flow restrictive aperture the fluid has a pressure p.sub.2 and a density .rho..sub.2. As can be seen in the graph of FIG. 1, the relationship between mass flow of a fluid and the fluid pressure upstream of a flow restrictive device is linear above a certain critical pressure and nonlinear below that critical pressure. More specifically, when the upstream pressure P.sub.1 is at least twice as great as the downstream pressure P.sub.2 (i.e., P.sub.1 /P.sub.2 .gtoreq.2,) the flow is said to be choked, and the flow rate is a function only of p.sub.1, .rho..sub.1 and the cross-sectional area A of the flow restrictive aperture. In general, choked flow is typically established by maintaining the upstream fluid supply at a pressure that is always at least about twice that of the fluid in the downstream processing chamber. In a choked flow regime, as the pressure of the fluid in the upstream reservoir increases, the density and flow rate of the fluid also increase.
As shown in the graph of FIG. 1, this relationship between flow rate and upstream pressure is linear so long as the upstream pressure remains at least twice that of the downstream pressure. However, when the upstream pressure is less than twice the downstream pressure (i.e., P.sub.1 /P.sub.2 &lt;2), the flow is said to be unchoked and the relationship between mass flow rate and downstream fluid pressure is nonlinear.
The pressure at which a precursor fluid (typically a gas) in the upstream reservoir of a choked flow system is maintained is, in part, a function of the vapor pressure of the precursor (liquid or solid) from which the gas is derived and the desired quantity of precursor to be delivered. Some precursors, typically liquids, used in vapor deposition processes have vapor pressures which are sufficiently high to ensure their delivery at a pressure which establishes choked flow and thus allows accurate measurement of mass flow. Other precursors, particularly low vapor pressure liquids and non-dissolved solids which must be sublimed to provide reactants in gaseous form, typically cannot be delivered at a sufficiently high pressure to ensure choked flow. As a result, the mass flow rate of such precursors cannot be accurately or reliably determined.
Until the present invention, no special provision has been made to permit a pressure-based MFC which has been calibrated for choked flow operation to operate in the non-linear, non-choked flow region. In the Model 1150 mass flow controller, for example, only the upstream fluid pressure is measured, although computer modeling is used to predict the mass flow in the non-linear range. In known choked-flow devices any measurements of flow rate have been assumed to be linearly related to the upstream pressure, as seen by the dotted line A in FIG. 1, even though the upstream pressure is actually less than twice the downstream pressure. In the non-choked flow regime, i.e., when the upstream pressure is less than twice the downstream pressure, the flow rate of the fluid varies as a function of the downstream fluid pressure and is independent of the upstream fluid pressure.
A need remains, therefore, for a mass flow controller which is suitable for use in the delivery of many types of precursor materials over a relatively wide range of operating temperatures, pressures and flow rates, without the need for frequent recalibration.